Equalizers and coactions of groups

• Autorzy: Martin Arkowitz , Mauricio Gutierrez
• Języki publikacji: EN

Abstrakty

EN

If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group $𝓔_{f}⊆ G*H$ be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism $p_{f} = p|𝓔_{f}:𝓔_{f} → G$. A right inverse (section) $G → 𝓔_{f}$ of $p_{f}$ is called a coaction on G. In this paper we study $𝓔_{f}$ and the sections of $p_{f}$. We consider the following topics: the structure of $𝓔_{f}$ as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and the resulting category of groups with a coaction and associativity of coactions.

Kategorie tematyczne

• 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
• 20F99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 171
• Numer: 2
• Strony: 155-165

Daty

wydano

2002

Twórcy

autor

Martin Arkowitz

• Mathematics Department, Dartmouth College, Hanover, NH 03755, U.S.A.

autor

Mauricio Gutierrez

• Mathematics Department, Tufts University, Medford, MA 02155, U.S.A.

Identyfikatory

DOI

10.4064/fm171-2-3